I got a pop-up saying I can find it in missions, enemies, and treasure chests. Are all Eridium spawns random? Does the Eridium supply have a cutoff? Do certain chests or enemies in certain areas/locations always drop Eridium? Can I reduce the Eridium costs at Crazy Earl's/the Black Market to maximize the Eridium I do find? Where are the best locations to farm Eridium? What are the most time- and cost-effective methods for farming it?

4 Answers
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So far it is unknown if there is a sure-fire way to obtain Eridium, but it is an uncommon-rare drop by certain enemies and rarely found in containers like lockers and washing machines. You can also obtain it by playing the slot machines at Moxxxi's place in Sanctuary.

Moxxxi's slot machines

According to this article the following is a list of potential payouts from playing the slot machines - in addition to randomly generated weapons and items of course;

x3 Bandits: Live grenade (Run!)

x3 7s: Customization skin

x3 Cherries: Green item

x3 Legs: Blue item

x3 Marcus: Purple item

x3 Borderlands logo: Orange item

x3 Eridium Bar (1): 4 Eridium

x3 Eridium Bars (2): 8 Eridium

x3 Eridium Stack (3): 16 Eridium (!!!!)

Any two with non-bell: White weapon

Any two with bell at end: Cash

It is worth noting that playing the slot machines at Moxxxi's place will get more expensive as you progress through the game, yet some of the items you can win by playing the slots scale with your character - this means that playing the slots at a lower level will cost less while still potentially providing benefit to you at the later levels.

Also of important note is that Eridium, like cash and ammo, is given to all players in a co-op session. So you can get four people together and spam the slot machine. Everyone benefits!
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EvilAmarant7xSep 19 '12 at 17:16

I have bought everything Crazy Earl has to offer and have then gone on to save a further 99 blocks of eridium. You cannot save any more than this. You can pick up the excess eridium, but it won't add to your tally.

Later on in the game, eridium drops become more common from defeated enemies. Earlier on you can scavenge plenty in Sanctuary, especially by checking inside the Crimson Raiders' HQ.

The warrior is by far the best place to farm Eridium if you need it for your alt characters. It drops 20-30 Eridium each time and can be defeated in about a minute with normal level 50 guns. Time is dropped to about 30 sec with good legendary weapons.